11.2 Arithmetic Sequences Day 1
Algebra 2 Intensified: 11.2 Day 1 Notes – Arithmetic Sequences
Formula for writing an equation of an arithmetic sequence:
Definition: An arithmetic sequence is a sequence in which each term after the first is found by adding a constant, called the common difference , d, to the previous term.
The nth term of an arithmetic sequence with first term and common difference is given by
Example 1: Fill in the next 3 terms. What is the common difference?
2, 5, 8, 11, 14, 17, ____, ____, ____
where is any positive integer. (* stands for the number of terms in the sequence)
Example 2: Fill in the next 3 terms. What is the common difference?
55, 49, 43, ____, ____, ____
Example 3: Write an equation for the nth term of the arithmetic sequence 8, 17, 26, 35, …
st
Method 1: 1 find and .
2
Example 4: a) Use either method to find the equation for the nth term of arithmetic sequence nd substitute and into .
b) Find rd
3 simplify.
c) Find the 120th term.
Method 2: Arithmetic sequences are linear so you can find the equation using .
Example 5: Find the 4 arithmetic means between 16 and 91. (this means the 4 missing terms between 16 & 91)
Example 6: Given and , find the equation of the arithmetic sequence and find the 3 arithmetic means between them.
Method 1:
Method 2:
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11.2 Arithmetic Sequences Day 1
Example 7: The table below shows typical costs for a construction company to rent a crane for one, two, three, or four months. Assuming that the arithmetic sequence continues, how much would it cost to rent a crane for 1 year?
Months
1
2
3
4
Cost $75,000
$90,000
$105,000
$120,000
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